Anova Table 7F7826
1. **Stating the problem:**
We have a dataset of yields for different varieties and doses of NPK fertilizer. We want to perform an ANOVA (Analysis of Variance) to determine if there are significant differences between the means of the groups.
2. **Understanding ANOVA:**
ANOVA tests the null hypothesis that all group means are equal against the alternative that at least one differs.
3. **Data structure:**
- Factors: Varietas (4 levels: Marihat, D X P PPKS 239, Dumpy, DXP 540)
- Doses (5 levels: 1.5, 1.75, 2, 2.25, 2.5 Kg/Pohon)
- Replicates: 3 per combination
4. **Steps to create ANOVA table:**
- Calculate the grand mean (overall average of all data).
- Calculate the sum of squares total (SST): sum of squared differences between each observation and grand mean.
- Calculate sum of squares for each factor (Varietas and Dose) and their interaction if needed.
- Calculate sum of squares error (SSE): SST minus sum of squares of factors.
- Calculate degrees of freedom (df) for each source.
- Calculate mean squares (MS) by dividing sum of squares by df.
- Calculate F-statistics: ratio of MS factor to MS error.
5. **Example ANOVA table format:**
| Source | df | Sum of Squares (SS) | Mean Square (MS) | F-value |
|--------------|-------------|---------------------|------------------|---------|
| Varietas | $a-1=3$ | $SS_{Varietas}$ | $MS_{Varietas}$ | $F_{Varietas}$ |
| Dose | $b-1=4$ | $SS_{Dose}$ | $MS_{Dose}$ | $F_{Dose}$ |
| Interaction | $(a-1)(b-1)=12$ | $SS_{Interaction}$ | $MS_{Interaction}$ | $F_{Interaction}$ |
| Error | $N - ab=60$ | $SS_{Error}$ | $MS_{Error}$ | |
| Total | $N-1=79$ | $SS_{Total}$ | | |
where $a=4$ varieties, $b=5$ doses, $N=80$ total observations.
6. **Calculations:**
You would sum the data accordingly to find means and sums of squares. This requires computational steps or software.
7. **Summary:**
The ANOVA table summarizes variance sources and tests significance of factors.
Since the user requested the ANOVA table from the given data, the above explains how to construct it. Actual numeric calculation requires processing the data values.